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Geometric group theory, geometric topology
I study infinite discrete groups by studying their actions on metric spaces, especially negatively curved (hyperbolic) metric spaces. The topology and geometry of 3-manifolds also figures heavily in my work, both directly and as inspiration.
- Filling virtually special subgroups, Appendix to The virtual Haken conjecture by Ian Agol. (with Ian Agol and Daniel Groves), Documenta Mathematica 18 (2013) 1045-1087.
- CAT(0) and CAT(-1) fillings of hyperbolic manifolds (with Koji Fujiwara), Journal of Differential Geometry 85 no. 2 (2010), 229–270.
- Virtually geometric words and Whitehead's algorithm, Mathematical Research Letters 17 no. 5 (2010), 917–925.
- Residual finiteness, QCERF, and fillings of hyperbolic groups (with I. Agol and D. Groves), Geometry & Topology 13 (2009), 1043–1073.
- Dehn filling in relatively hyperbolic groups (with D. Groves), Israel Journal of Mathematics 168 (2008), 317–429.
- Geometry of pseudocharacters, Geometry & Topology 9 (2005), 1147–1185.
- Algorithmic detection and description of hyperbolic structures on 3-manifolds with solvable word problem, Geometry & Topology 6 (2002), 1–26.